| YANG Hongli,YANG Liangui,SONG Jinbao,Hou Yijun. 2009. Higher-order Boussinesq-type equations for interfacial waves in a two-fluid system. Acta Oceanologica Sinica, (4):118－124 |
| Higher-order Boussinesq-type equations for interfacial waves in a two-fluid system |
| Higher-order Boussinesq-type equations for interfacial waves in a two-fluid system |
| Received:July 18, 2007 Revised:August 30, 2008 |
| DOI： |
| Key words:two-layer fluid interfacial waves Boussinesq-type equations enhanced equations fully nonlinear |
| 中文关键词: two-layer fluid interfacial waves Boussinesq-type equations enhanced equations fully nonlinear |
| 基金项目:Knowledge Innovation Programs of the Chinese Academy of Sciences under contract Nos KZCX2-YW-201 and KZCX1-YW-12, Natural Science Fund supported by the Educational Department of Inner Mongolia under contract Nos NJzy080005, and NJ09011, A Grant from Science Fund for Young Scholars of Inner Mongolia University under contract No.ND0801. |
| Author Name | Affiliation | E-mail | | YANG Hongli | School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
Key Laboratory of Ocean Circulation and Waves, Chinese Academy of Sciences, Qingdao 266071, China | | | YANG Liangui | School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China | lgyang@imu.edu.cn | | SONG Jinbao | Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
Key Laboratory of Ocean Circulation and Waves, Chinese Academy of Sciences, Qingdao 266071, China | | | Hou Yijun | Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
Key Laboratory of Ocean Circulation and Waves, Chinese Academy of Sciences, Qingdao 266071, China | |
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| Abstract: |
| Interfacial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. A set of higher-order Boussinesq-type equations in terms of the depth-averaged velocities accounting for stronger nonlinearity are derived. When the small parameter measuring frequency dispersion keeping up to lower-order and full nonlinearity are considered, the equations include the Choi and Camassa's results (1999). The enhanced equations in terms of the depth-averaged velocities are obtained by applying the enhancement technique introduced by Madsen et al. (1991) and Schaffer and Madsen (1995a). It is noted that the equations derived from the present study include, as special cases, those obtained by Madsen and Schaffer (1998). By comparison with the dispersion relation of the linear Stokes waves, we found that the dispersion relation is more improved than Choi and Camassa's (1999) results, and the applicable scope of water depth is deeper. |
| 中文摘要: |
| Interfacial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. A set of higher-order Boussinesq-type equations in terms of the depth-averaged velocities accounting for stronger nonlinearity are derived. When the small parameter measuring frequency dispersion keeping up to lower-order and full nonlinearity are considered, the equations include the Choi and Camassa's results (1999). The enhanced equations in terms of the depth-averaged velocities are obtained by applying the enhancement technique introduced by Madsen et al. (1991) and Schaffer and Madsen (1995a). It is noted that the equations derived from the present study include, as special cases, those obtained by Madsen and Schaffer (1998). By comparison with the dispersion relation of the linear Stokes waves, we found that the dispersion relation is more improved than Choi and Camassa's (1999) results, and the applicable scope of water depth is deeper. |
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